Question: Simplify the following expression: $ r = \dfrac{-8}{5} + \dfrac{-6x + 9}{x - 5} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x - 5}{x - 5}$ $ \dfrac{-8}{5} \times \dfrac{x - 5}{x - 5} = \dfrac{-8x + 40}{5x - 25} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-6x + 9}{x - 5} \times \dfrac{5}{5} = \dfrac{-30x + 45}{5x - 25} $ Therefore $ r = \dfrac{-8x + 40}{5x - 25} + \dfrac{-30x + 45}{5x - 25} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{-8x + 40 - 30x + 45}{5x - 25} $ $r = \dfrac{-38x + 85}{5x - 25}$